Equation of ellipse whose vertices are ( pm 5,0) and foci are ( pm 4,0) is

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10-2. Parabola, Ellipse, Hyperbola

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The equation of the ellipse whose vertices are $( \pm 5,\;0)$ and foci are $( \pm 4,\;0)$ is

A

$9{x^2} + 25{y^2} = 225$

B

$25{x^2} + 9{y^2} = 225$

C

$3{x^2} + 4{y^2} = 192$

D

None of these

Solution

(a) Vertices $( \pm 5,\,0) \equiv ( \pm a,\,0)$ $⇒ a = 5$

Foci $( \pm 4,\,0) \equiv ( \pm ae,\,0)$

$e = \frac{4}{5}$,

$b = (5)\,\left( {\frac{3}{5}} \right) = 3$

Hence equation is $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1$

$i.e.$, $9{x^2} + 25{y^2} = 225$.

Standard 11

Mathematics

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